# Aptitude Questions: Ratio & Proportion

• An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.X, and the difference between Q and R’s share is Rs.3000. Find the total amount of money?
A.11000
B.12400
C.13200
D.14300
E.None of these

Explanation :
12a-7a = 3000
5a = 3000
a = 600
7a-4a = x
3a = x
x = 1800
22*600 = 13200
• If a certain amount X is divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets 1/3 of what C gets, which of the following is true
A.C’s Share = 1053 and X = 1666
B.A’s Share = 238 and X = 1638
C.B’s Share = 234 and X = 1666
D.C’s Share = 1053 and X = 1638
E.A’s Share = 351 and X = 1638

Answer – D.C’s Share = 1053 and X = 1638
Explanation :
A= 2/3 B; B= 1/3C;
A:B = 2:3 ; B:C = 1:3;
A:B:C = 2:3:9
C = 9/14 * 1638 = 1053
• Seats for Mathematics, Science and arts in a school are in the ratio 5:7:8. There is a proposal to increase these seats by X%, Y% and Z% respectively. And the ratio of increased seats is 2:3:4, which of the following is true?
A.X = 50; Z = 40
B.Y = 40; Z = 50
C.X = 40; Z = 75
D.X = 50; Z = 40
E.Y = 50; X = 75

Answer – C.X = 40; Z = 75
Explanation :
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x)
i.e., (140/100 * 5x), (150/100 * 7x) and (175/100 * 8x)
i.e., 7x, 21x/2 and 14x
Required ratio = 7x:21x/2:14x
= 14x : 21x : 28x = 2:3:4
• An amount of money is to be distributed among P, Q and R in the ratio of 7:4:5 respectively. If the total share of P and R is 4 times the share of Q, what is definitely Q’s share?
A.2000
B.4000
C.6000
E.None of these

Explanation :
Total sum not given
• Two candles of same height are lighted at the same time. The first is consumed in 3 hours and second in 2 hours. Assuming that each candles burns at a constant rate, in how many hours after being lighted, the ratio between the first and second candles becomes 2:1?
A.2 hour
B.2.5 hour
C.4 hour
D.4.5 hour
E.None of these

Explanation :
Height of both candles are same i.e. h
First one takes 6 hours to burn completely, so in one hour = h/3
Similarly second one will burn in one hour = h/2
Let after t time, ratio between their height is 2:1
so, remaining height of first candle = h – t*(h/3)
similarly for second candle = h – t*(h/2)
ratio given 2:1,
h – t*(h/3) / h – t*(h/2) = 2/1
Solving we get t = 9/2 = 4.5
• If A and B together have a certain amount X and if 4/15 of A’s amount is equal to 2/5 of B’s amount, which of the following is true?
A.A = 1767; X = 2675
B.B = 1070; X = 2895
C.A = 1767; X = 2945
D.B = 1158; X = 2585
E.A = 1605; X = 2945

Answer – C.A = 1767; X = 2945
Explanation :
4/15 * A = 2/5 * B
A= 2/3 B;
A:B = 3:2;
A = 3/5 * 2945 = 1767
• A sum of Rs.4880 was divided among boys and girls in such a way that each boy gets Rs.44.50 and each girl get Rs. 55.25. If the total number of girls and boys is 100, find the number of girls?
A.60
B.50
C.40
D.30
E.None of these

Explanation :
x+y=100 ————– (i)
44.50x + 55.25y = 4880 ————– (ii)
Solving (i) and (ii) Y = 40
• The income of Vinay and Prakash are in the ratio of 4:5 and their expenditure is in the ratio of 2:3. If each of them saves 5000, then find their income.
A.11000, 8550
B.12000, 7750
C.15000, 8750
D.13000, 9780
E.None of these

Explanation :
4x – 2y = 5000 and 5x – 3y = 5000.
X = 8750, so income = 8750 and 15000
• If the ratio of the first to second is 2:3 and that of the second to the third is 5: 8, then which of the following is true,
A.Sum = 98; A = 48
B.Sum = 147; B = 30
C.Sum = 147; C = 45
D.Sum = 98; B = 30
E.Sum = 98; C = 72

Answer – D.Sum = 98; B = 30
Explanation :
A:B:C = 10:15:24
If sum = 98, B = 15/49 * 98 = 30
• A bag contains 25p coins, 50p coins and 1 rupee coins whose values are in the ratio of 8:4:2.If the total values of coins isX and the total amount in rupees is Y,thenwhich of the following is true
A.X = 840; Y = 260
B.X = 966; Y = 345
C.X = 840; Y = 280
D.X = 740; Y = 260
E.None of these